It is a fairly new field. I like the concept of ORCH OR (Orchestrated Objective Reduction) proposed by Roger Penrose and Stuart Hameroff.
It proposes a form of quantum data processing at nanoscale and considers the role MTs play in neural and cellular data processing in addition to cell division (mitosis) and motility (pseudopodia)
Microtubules Are an Important Determinant of Cell Architecture
Microtubules are nearly ubiquitous components of the cytoskeleton in eukaryotes. They play key roles in [intracellular transport]
Microtubules are very abundant in the nervous system, and tubulin subunits of microtubules may constitute more than 10% of total brain protein.
The number of MTs contained in the brain alone makes them prime contenders for an emergent cognitive data processing system.
p.s. see also Microtubules the seat of Consciousness - #237 by citizenschallengev4